“Striped” rectangular rigid box with Hermitian and non-Hermitian PT symmetric potentials

Eigenspectra of a spinless particle inside a rigid rectangular box subject to diverse inner potential distributions are investigated under both Hermitian and non-Hermitian antiunitary PT (composite parity and time-reversal) symmetric regimes. Four “stripes” conjoined widthwise, spanning the box bear...

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Bibliographic Details
Published in:Journal of mathematical physics 2021-10, Vol.62 (10)
Main Authors: Kulkarni, Shailesh, Pathak, Rajeev K.
Format: Article
Language:English
Subjects:
Breakdown
Broken symmetry
Charged particles
Electric fields
Mathematical analysis
Physics
Symmetry
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Summary:Eigenspectra of a spinless particle inside a rigid rectangular box subject to diverse inner potential distributions are investigated under both Hermitian and non-Hermitian antiunitary PT (composite parity and time-reversal) symmetric regimes. Four “stripes” conjoined widthwise, spanning the box bearing piecewise constant potentials, are studied whose exact energy eigenspectra are obtained employing matrix mechanics. Diverse real-Hermitian and complex non-Hermitian PT symmetric potential compositions are considered separately and in conjunction, unraveling peculiar retention and breakdown scenarios engendered by PT symmetry. Some states exhibit remarkable crossovers of symmetry “making” and “breaking”: a broken PT gets reinstated, while higher levels “collude” to continue with symmetry breaking. Furthermore, a charged particle in a PT symmetric electric field imposed on the striped potential backdrop reveals peculiar symmetry retention and breakdown scenarios. Depictions of prominent probability-density redistributions under the norm conserving unitary regime, as well as non-conserving post-PT-breakdown, are presented.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0065899